Investigation: Make My Graph



Investigation: Make My Graph

Step 1 Make an accurate graph of the parent function y = x2 on the coordinate plane below.

Make a Table On the Calculator: y = x2

|x |y |

|-2 | |

|-1 | |

|0 | |

|1 | |

|2 | |

Step 2 On your calculator graph the following equations. Then describe what happened to the parent function.

a. y = x2 + 3 b. y = x2 – 7 c. y = (x + 2) 2

d. y = (x – 5) 2 e. y = (x + 3) 2 -1

Step 3 Each graph below shows the graph of the parent function f(x) = x2 with the vertex at (0,0). Use your findings from step 2 to write a quadratic equation that produces the congruent graph with plotted points. Check your equation on your calculator.

a. b. c.

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d. e. f.

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g. h. i. *Challenge*

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Step 4 State what h, k and the 2 do to the graphs.

This could also be written as

____________________________

Or

____________________________

Review it all together:

Functions can come in all shapes and sizes. So, sometimes we just call graphs y = f(x) if it is just any given graph, such as the one below.

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Step 9 Write the equation of each transformed graph. The parent function is the one with dotted lines.

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Example 1: The graph shows a portion of a parabola. It represents a diver’s position (horizontal and vertical distance) from the edge of a pool as he dives from a 5 ft long board 25 ft above the water.

a. Identify points on the graph that represent when the diver leaves the board, when he reaches his maximum height, and when he enters the water.

b. Sketch a graph of the diver’s position if he dives from a 10 ft long board, 10 feet above the water. (Assume that he leaves the board at the same angle and with the same force.)

c. In the scenario described in part b, what is the diver’s position when he reaches his maximum height?

Example 2: Where is the vertex of the parabola represented by y = (x + 0)2 + 4?

Name: ________________________________

Exit Ticket 2.4

1. The parabola y = x2 is shifted to have a vertex of (-2, 4). What is an equation of this new parabola?

2. Describe the location of a parabola y = f(x – 3) + 4 relative to y = f(x)

Name: ________________________________

Exit Ticket 2.4

1. The parabola y = x2 is shifted to have a vertex of (-2, 4). What is an equation of this new parabola?

2. Describe the location of a parabola y = f(x – 3) + 4 relative to y = f(x)

Name: ____________________________ Homework 2.4

Quadratics and Translations (Section 4.4 in textbook)

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